Необходимые библиотеки
Разработано на основе материалов Bojanowski and Jasny (2025), URL: statnet.org
# install.packages("igraph")
library(igraph)##
## Attaching package: 'igraph'## The following objects are masked from 'package:dplyr':
##
## as_data_frame, groups, union## The following objects are masked from 'package:stats':
##
## decompose, spectrum## The following object is masked from 'package:base':
##
## union# install.packages("intergraph")
library(intergraph) # для конвертации между форматамиУзнать больше о пакете igraph можно на сайте разработчиков. Обзор основных
функций приводится в виньетке.
Базовый функционал igraph
Создание простых графов
make_graph(c(1, 2, 2, 3, 3, 4), directed = FALSE) %>% plot()
make_graph(~ A - B, B - C:D:E) %>% plot()
g = make_graph(~ A --+ B, B +-- C, A --+ D:E, B --+ A)
g## IGRAPH 4fc6eb6 DN-- 5 5 --
## + attr: name (v/c)
## + edges from 4fc6eb6 (vertex names):
## [1] A->B A->D A->E B->A C->Bplot(g) # граф с прошлой пары
Загрузка данных и конвертация в граф
load("introToSNAinR.Rdata")
summary(contig_1993)## Network attributes:
## vertices = 186
## directed = FALSE
## hyper = FALSE
## loops = FALSE
## multiple = FALSE
## total edges = 534
## missing edges = 0
## non-missing edges = 534
## density = 0.03103749
##
## Vertex attributes:
##
## State.Abb:
## character valued attribute
## attribute summary:
## the 10 most common values are:
## AAB AFG ALB ALG AND ANG ARG ARM AUL AUS
## 1 1 1 1 1 1 1 1 1 1
##
## State.Num:
## integer valued attribute
## 186 values
## vertex.names:
## character valued attribute
## 186 valid vertex names
##
## Edge attributes:
##
## ContType:
## numeric valued attribute
## attribute summary:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.000 1.000 1.000 2.457 4.000 5.000
##
## Network edgelist matrix:
## [,1] [,2]
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## [534,] 182 181Наивный перевод из network в graph: по
составным частям
Синтаксис graph_from_{...} позволяет создавать графы из
разных форматов представления данных, например: матриц смежности
(adjacency_matrix), датафреймов (data_frame)
или списков рёбер в формате matrix, как ниже:
guerre = network::as.edgelist(contig_1993) %>% graph_from_edgelist(directed = FALSE)
guerre## IGRAPH 9a6678d U--- 185 534 --
## + edges from 9a6678d:
## [1] 1-- 2 1-- 3 1-- 4 1--16 1--68 3-- 4 3-- 5 3-- 6 3-- 7 4-- 5
## [11] 4-- 6 4-- 7 4--16 4--17 4--19 5-- 6 5-- 7 5--24 6-- 7 6--15
## [21] 6--24 6--25 7--19 7--21 7--24 8-- 9 8--11 8--12 8--13 8--25
## [31] 8--26 8--27 9--10 9--11 9--12 9--13 9--14 9--25 9--26 10--11
## [41] 10--12 10--13 10--15 10--25 11--13 11--14 11--15 11--25 11--26 12--13
## [51] 12--14 12--15 12--25 12--26 13--14 13--15 13--25 13--26 14--15 14--25
## [61] 15--25 16--17 16--18 16--19 17--18 17--19 18--19 18--20 18--21 18--22
## [71] 19--20 19--21 20--21 20--22 21--22 21--23 21--24 22--23 22--24 23--24
## [81] 24--25 24--28 24--29 24--30 25--26 25--30 26--27 26--30 27--30 28--29
## + ... omitted several edgesПроблема: кажется, мы потеряли один узел (почему?)
Конвертация с помощью intergraph
guerre_full = asIgraph(contig_1993)
guerre_full## IGRAPH a19d05e U--- 186 534 --
## + attr: na (v/l), State.Abb (v/c), State.Num (v/n), vertex.names (v/c),
## | ContType (e/n), na (e/l)
## + edges from a19d05e:
## [1] 1-- 2 1-- 3 1-- 4 1--16 1--68 3-- 4 3-- 5 3-- 6 3-- 7 4-- 5
## [11] 4-- 6 4-- 7 4--16 4--17 4--19 5-- 6 5-- 7 5--24 6-- 7 6--15
## [21] 6--24 6--25 7--19 7--21 7--24 8-- 9 8--11 8--12 8--13 8--25
## [31] 8--26 8--27 9--10 9--11 9--12 9--13 9--14 9--25 9--26 10--11
## [41] 10--12 10--13 10--15 10--25 11--13 11--14 11--15 11--25 11--26 12--13
## [51] 12--14 12--15 12--25 12--26 13--14 13--15 13--25 13--26 14--15 14--25
## [61] 15--25 16--17 16--18 16--19 17--18 17--19 18--19 18--20 18--21 18--22
## + ... omitted several edgesplot(guerre_full, layout = layout_nicely,
vertex.label = V(guerre_full)$State.Abb,
vertex.size = 3,
vertex.label.cex = 0.5,
vertex.label.dist = 1)
Продвинутые характеристики сетей
Основные метрики сети в igraph
Описательная статистика
# Узлы
vcount(guerre_full)## [1] 186# Рёбра
ecount(guerre_full)## [1] 534# Диады можно посчитать вручную. Направленный граф:
vcount(guerre_full) * (vcount(guerre_full) - 1)## [1] 34410# Диады для ненаправленного графа (наш случай):
vcount(guerre_full) * (vcount(guerre_full) - 1) / 2## [1] 17205Метрики центральности
# Degree / Степень связности
deg = degree(guerre_full, mode = "all")
# Indegree, outdegree (имеет смысл только для направленных графов)
ideg = degree(guerre_full, mode = "in")
odeg = degree(guerre_full, mode = "out")
# Betweenness / Степень посредничества
bet = betweenness(guerre_full, directed = F)
# Closeness
clo = closeness(guerre_full, mode = "all")
# Eigenvector centrality
eig = eigen_centrality(guerre_full, directed = F)$vector
data.frame(deg = deg, ideg = ideg, odeg = odeg, bet = bet, clo = clo, eig = eig) %>% skimr::skim()| Name | Piped data |
| Number of rows | 186 |
| Number of columns | 6 |
| _______________________ | |
| Column type frequency: | |
| numeric | 6 |
| ________________________ | |
| Group variables | None |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| deg | 0 | 1.00 | 5.74 | 3.49 | 0 | 4 | 5.00 | 7.00 | 22.00 | ▆▇▂▁▁ |
| ideg | 0 | 1.00 | 5.74 | 3.49 | 0 | 4 | 5.00 | 7.00 | 22.00 | ▆▇▂▁▁ |
| odeg | 0 | 1.00 | 5.74 | 3.49 | 0 | 4 | 5.00 | 7.00 | 22.00 | ▆▇▂▁▁ |
| bet | 0 | 1.00 | 378.72 | 904.81 | 0 | 0 | 26.86 | 291.87 | 7944.28 | ▇▁▁▁▁ |
| clo | 5 | 0.97 | 0.00 | 0.00 | 0 | 0 | 0.00 | 0.00 | 0.00 | ▅▆▇▆▁ |
| eig | 0 | 1.00 | 0.10 | 0.17 | 0 | 0 | 0.02 | 0.12 | 1.00 | ▇▁▁▁▁ |
# Почему есть пропущенные значения для степени близости?
# Centralization measures
centr_degree(guerre_full, mode = "in", normalized = TRUE)## $res
## [1] 5 1 5 8 5 7 7 7 8 6 8 8 9 6 7 5 4 6 7 4 7 5 3 10 12
## [26] 8 3 2 5 9 5 3 3 5 2 7 2 6 6 3 14 3 2 5 8 2 2 16 12 8
## [51] 7 4 5 15 1 5 6 4 7 8 2 4 10 6 6 2 6 22 7 9 8 10 5 4 5
## [76] 7 7 9 7 12 0 1 4 2 4 1 7 6 5 4 8 5 6 6 3 2 5 4 8 9
## [101] 6 5 6 5 9 5 5 11 3 4 6 5 7 5 5 9 8 4 3 6 4 1 4 2 3
## [126] 4 1 5 4 9 6 10 11 14 16 8 10 7 5 5 7 15 7 5 7 7 5 8 6 6
## [151] 4 4 5 7 18 2 3 4 4 6 11 2 5 2 6 1 1 2 7 4 5 6 8 2 2
## [176] 6 10 2 4 0 1 2 0 0 2 0
##
## $centralization
## [1] 0.08788143
##
## $theoretical_max
## [1] 34410centr_eigen(guerre_full, directed = F, normalized = TRUE)## $vector
## [1] 1.165389e-01 1.274446e-02 1.686722e-02 1.957601e-02 5.658355e-03
## [6] 5.974568e-03 6.490791e-03 7.018465e-04 8.228612e-04 7.345685e-04
## [11] 8.670060e-04 8.670060e-04 9.524734e-04 7.345685e-04 1.314824e-03
## [16] 1.647764e-02 4.989506e-03 3.560277e-03 6.011541e-03 1.444095e-03
## [21] 2.432925e-03 1.200474e-03 7.071547e-04 2.833025e-03 1.892933e-03
## [26] 7.740745e-04 2.415303e-04 3.597214e-04 4.563691e-04 7.327007e-04
## [31] 1.655161e-04 1.124247e-04 8.220565e-05 1.298266e-04 9.432420e-05
## [36] 3.629392e-01 8.576023e-02 3.544852e-01 3.225323e-01 1.750453e-01
## [41] 4.212768e-01 8.279326e-02 4.365299e-02 1.911604e-01 1.175827e-01
## [46] 5.892855e-02 1.619899e-02 8.568550e-01 7.496100e-01 2.080150e-01
## [51] 1.227737e-01 2.183454e-01 1.821322e-01 2.182257e-01 2.386470e-02
## [56] 7.917775e-02 7.386244e-02 4.911199e-02 8.196923e-02 8.949123e-02
## [61] 1.875056e-02 6.900305e-02 1.574433e-01 1.133676e-01 1.282971e-01
## [66] 5.381142e-02 1.253427e-01 1.000000e+00 5.764095e-01 6.739811e-01
## [71] 6.171600e-01 3.667243e-01 3.726344e-01 1.217456e-01 2.337585e-01
## [76] 2.640135e-01 5.252244e-01 6.864561e-01 4.991845e-01 7.787257e-01
## [81] 1.009510e-19 5.877742e-04 3.764733e-03 1.010382e-03 3.764733e-03
## [86] 5.877742e-04 2.294845e-02 5.374775e-03 7.782116e-03 2.014964e-02
## [91] 4.133784e-02 4.502223e-03 3.864450e-03 9.232948e-03 9.728116e-04
## [96] 5.289929e-04 4.150946e-03 3.707128e-03 1.328771e-02 1.273302e-02
## [101] 4.640321e-03 1.563059e-02 3.399885e-02 5.636564e-03 1.473807e-02
## [106] 1.344698e-02 1.838619e-02 1.003883e-02 3.205006e-03 4.530578e-03
## [111] 2.646671e-02 3.367427e-02 4.290661e-02 3.848512e-02 3.245648e-03
## [116] 2.298843e-03 3.765543e-03 7.950921e-04 1.761015e-03 5.490997e-04
## [121] 8.986327e-04 6.004840e-05 6.570626e-04 3.114451e-04 6.012343e-04
## [126] 1.590839e-03 1.758668e-04 1.608176e-03 3.054549e-02 1.253853e-01
## [131] 1.218559e-01 1.526366e-01 7.526938e-02 2.304333e-01 3.850713e-01
## [136] 1.332883e-01 1.579871e-01 1.183166e-01 9.784722e-02 7.435898e-02
## [141] 1.200002e-01 1.503675e-01 4.970117e-02 7.633539e-02 9.197175e-02
## [146] 9.197175e-02 7.130753e-02 8.731210e-02 1.043701e-01 2.086274e-01
## [151] 5.974743e-02 7.258307e-02 7.435315e-02 2.345784e-01 2.950413e-01
## [156] 1.416230e-01 6.125789e-02 1.830695e-01 1.830695e-01 1.959287e-01
## [161] 7.096244e-02 4.002540e-02 8.618707e-02 1.374308e-02 5.470819e-02
## [166] 7.760305e-03 7.760305e-03 4.002540e-02 3.433179e-02 1.833544e-02
## [171] 4.958776e-02 5.102796e-02 3.271694e-02 7.580463e-03 1.114430e-02
## [176] 6.918967e-02 3.660098e-02 4.555993e-03 5.060324e-03 1.009510e-19
## [181] 6.124970e-05 5.600847e-04 1.009510e-19 1.009510e-19 4.555993e-03
## [186] 1.009510e-19
##
## $value
## [1] 9.144285
##
## $options
## $options$bmat
## [1] "I"
##
## $options$n
## [1] 186
##
## $options$which
## [1] "LA"
##
## $options$nev
## [1] 1
##
## $options$tol
## [1] 0
##
## $options$ncv
## [1] 0
##
## $options$ldv
## [1] 0
##
## $options$ishift
## [1] 1
##
## $options$maxiter
## [1] 3000
##
## $options$nb
## [1] 1
##
## $options$mode
## [1] 1
##
## $options$start
## [1] 1
##
## $options$sigma
## [1] 0
##
## $options$sigmai
## [1] 0
##
## $options$info
## [1] 0
##
## $options$iter
## [1] 3
##
## $options$nconv
## [1] 1
##
## $options$numop
## [1] 40
##
## $options$numopb
## [1] 0
##
## $options$numreo
## [1] 30
##
##
## $centralization
## [1] 0.9122258
##
## $theoretical_max
## [1] 184Плотность, диаметр, компоненты связности в igraph
Плотность / density
edge_density(guerre_full)## [1] 0.03103749Диаметр / diameter
diameter(guerre_full, directed = FALSE, unconnected = TRUE) ## [1] 14Компонента связности / component connectivity
comp = components(guerre_full, mode = "strong")
# Количество компонент
comp$no## [1] 6# Размеры компонент
comp$csize## [1] 181 1 1 1 1 1# Членство узлов в компонентах
comp$membership## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [75] 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [112] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 4 5 1
## [186] 6split(V(guerre_full)$State.Abb, comp$membership)## $`1`
## [1] "USA" "CAN" "BHM" "CUB" "HAI" "DOM" "JAM" "TRI" "BAR" "DMA" "GRN" "SLU"
## [13] "SVG" "AAB" "SKN" "MEX" "BLZ" "GUA" "HON" "SAL" "NIC" "COS" "PAN" "COL"
## [25] "VEN" "GUY" "SUR" "ECU" "PER" "BRA" "BOL" "PAR" "CHL" "ARG" "URU" "UKG"
## [37] "IRE" "NTH" "BEL" "LUX" "FRN" "MNC" "LIE" "SWZ" "SPN" "AND" "POR" "GMY"
## [49] "POL" "AUS" "HUN" "CZR" "SLO" "ITA" "SNM" "MLT" "ALB" "MAC" "CRO" "YUG"
## [61] "BOS" "SLV" "GRC" "CYP" "BUL" "MLD" "ROM" "RUS" "EST" "LAT" "LIT" "UKR"
## [73] "BLR" "ARM" "GRG" "AZE" "FIN" "SWD" "NOR" "DEN" "CAP" "STP" "GNB" "EQG"
## [85] "GAM" "MLI" "SEN" "BEN" "MAA" "NIR" "CDI" "GUI" "BFO" "LBR" "SIE" "GHA"
## [97] "TOG" "CAO" "NIG" "GAB" "CEN" "CHA" "CON" "DRC" "UGA" "KEN" "TAZ" "BUI"
## [109] "RWA" "SOM" "DJI" "ETH" "ERI" "ANG" "MZM" "ZAM" "ZIM" "MAW" "SAF" "NAM"
## [121] "LES" "BOT" "SWA" "MAG" "COM" "MAS" "SEY" "MOR" "ALG" "TUN" "LIB" "SUD"
## [133] "IRN" "TUR" "IRQ" "EGY" "SYR" "LEB" "JOR" "ISR" "SAU" "YEM" "KUW" "BAH"
## [145] "QAT" "UAE" "OMA" "AFG" "TKM" "TAJ" "KYR" "UZB" "KZK" "CHN" "MON" "TAW"
## [157] "PRK" "ROK" "JPN" "IND" "BHU" "PAK" "BNG" "MYA" "SRI" "MAD" "NEP" "THI"
## [169] "CAM" "LAO" "DRV" "MAL" "SIN" "BRU" "PHI" "INS" "AUL" "PNG" "VAN" "SOL"
## [181] "FSM"
##
## $`2`
## [1] "ICE"
##
## $`3`
## [1] "NEW"
##
## $`4`
## [1] "FIJ"
##
## $`5`
## [1] "MSI"
##
## $`6`
## [1] "WSM"plot(guerre_full, vertex.color = comp$membership)
Продвинутые метрики в network
igraph и network / sna
конфликтуют между собой, поэтому сначала необходимо отключить один из
пакетов
detach("package:igraph", unload = TRUE)
library(network)##
## 'network' 1.19.0 (2024-12-08), part of the Statnet Project
## * 'news(package="network")' for changes since last version
## * 'citation("network")' for citation information
## * 'https://statnet.org' for help, support, and other informationlibrary(sna)## Loading required package: statnet.common##
## Attaching package: 'statnet.common'## The following objects are masked from 'package:base':
##
## attr, order, replace## sna: Tools for Social Network Analysis
## Version 2.8 created on 2024-09-07.
## copyright (c) 2005, Carter T. Butts, University of California-Irvine
## For citation information, type citation("sna").
## Type help(package="sna") to get started.Загрузим датасет с прошлой пары — про связи детей в классе
edgeNet = read.csv("classroom-edges.csv", header = T, stringsAsFactors = F) %>% network(directed = T)Плотность / density
gden(edgeNet)## [1] 0.1466667Диаметр / diameter
geodist(edgeNet)$gdist %>% max(., na.rm = TRUE)## [1] InfОчень грустно — диаметр оказался бесконечным (существуют бесконечные расстояния). Скорее всего, в графе несколько сильно связных подграфов вместо одного. Простое решение — посчитать диаметр для ненаправленного графа.
a = network(edgeNet[,], directed = F)
geodist(a)$gdist %>% max(., na.rm = TRUE)## [1] 4Компонента связности / component connectivity
sna::components(edgeNet, connected = "strong")## [1] 8# Несколько компонент, посчитаем диаметр для крупнейшей
component.dist(edgeNet, connected = "strong")## $membership
## [1] 1 1 1 2 2 1 2 3 4 5 6 1 1 1 1 1 1 1 1 7 7 7 1 8 1
##
## $csize
## [1] 14 3 1 1 1 1 3 1
##
## $cdist
## [1] 5 0 2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0largest = component.largest(edgeNet, result = "graph")
largest## 1003 1006 1009 1018 1039 1042 1045 1048 1051 1054 1057 1060 1072 1078
## 1003 0 0 0 1 0 0 0 0 1 0 0 0 1 0
## 1006 0 0 1 0 0 1 0 0 0 0 1 0 0 1
## 1009 0 1 0 0 0 0 0 0 0 0 1 0 0 1
## 1018 0 0 0 0 0 1 0 1 1 0 0 1 1 0
## 1039 0 0 0 1 0 1 0 0 0 0 0 0 0 0
## 1042 0 1 0 1 1 0 0 0 1 0 0 0 0 0
## 1045 0 0 0 1 0 1 0 0 0 0 0 0 0 0
## 1048 0 0 0 1 0 1 1 0 1 1 0 0 0 0
## 1051 0 0 0 1 0 1 1 1 0 1 0 0 0 0
## 1054 0 0 0 1 1 0 0 1 1 0 0 0 1 0
## 1057 0 0 1 0 0 0 0 0 0 0 0 0 0 1
## 1060 1 0 0 1 0 1 0 0 1 0 0 0 0 0
## 1072 1 0 0 1 0 0 0 0 1 0 0 0 0 0
## 1078 0 1 1 0 0 0 0 0 0 0 1 0 0 0geodist(network(largest))$gdist %>% max(., na.rm = TRUE)## [1] 6Визуализации больших сетей
Визуализации на базе network
gplot(contig_1993, gmode = "graph",
label = colnames(contig_1993[,]),
label.cex = 0.5, label.col = "blue")
#quartz() или windows()
#coords = gplot(contig_1993, interactive = TRUE)
#gplot(contig_1993, coord = coords)
gplot(contig_1993, gmode = "graph",
label = ifelse(evcent(contig_1993) > 0.1, colnames(contig_1993[,]), ""),
label.cex = 0.7, label.col = "blue",
displayisolates = F, vertex.cex = 10 * evcent(contig_1993))
Визуализация igraph
detach("package:sna", unload = TRUE)
detach("package:network", unload = TRUE)
library(igraph)##
## Attaching package: 'igraph'## The following objects are masked from 'package:dplyr':
##
## as_data_frame, groups, union## The following objects are masked from 'package:stats':
##
## decompose, spectrum## The following object is masked from 'package:base':
##
## unionplot(
guerre_full,
vertex.label = ifelse(betweenness(guerre_full) > 1000, V(guerre_full)$State.Abb, NA),
vertex.size = betweenness(guerre_full) / 500,
vertex.label.cex = 0.7,
vertex.label.color = "blue",
main = "Graph with Betweenness Centrality Labels"
)
Создадим интерактивный график. Документацию по пакету можно найти здесь: https://datastorm-open.github.io/visNetwork/
#install.packages("visNetwork")
library(visNetwork)
visIgraph(guerre_full) %>%
visOptions(highlightNearest = T, nodesIdSelection = T) %>%
visLayout(randomSeed = 123)# Custom
nodes = data.frame(
id = 1:vcount(guerre_full),
label = V(guerre_full)$State.Abb,
title = paste("Node", V(guerre_full)$State.Abb),
size = 25,
color = "orange",
font.size = 14,
font.color = "black"
)
edges = data.frame(
from = as.vector(get.edgelist(guerre_full)[,1]),
to = as.vector(get.edgelist(guerre_full)[,2]),
color = "gray"
)
visNetwork(nodes, edges) %>%
visOptions(
highlightNearest = list(enabled = TRUE, hover = TRUE),
nodesIdSelection = TRUE,
) %>% visPhysics(stabilization = FALSE) %>%
visLayout(randomSeed = 123)Групповое задание — заявка на проект
Проектные заявки сдавать в форму по этой ссылке
Структура заявки на проект:
ФИО двух-трёх участников (один человек — одна группа, по одиночке нельзя). Если вы не можете найти себе пару, напишите мне на почту aganov.artem@yandex.ru как можно скорее.
Исследовательский вопрос — не может быть задан в форме да/нет; ваша задача узнать, как/почему нечто происходит и/или провести разведочный анализ.
Структура данных и ссылка на них. Из приложенных вами сведений должно быть понятно, откуда вы взяли ваши данные, как они соотносятся с вашим исследовательским вопросом, а также как они внутренне организованы.
Просто приложить ссылку на датасет без кодбука и описания не имеет смысла — лучше ссылка на сайт, где будут выложены все эти вещи. Если существует только файл с данными, напишите в нескольких предложениях, какие переменные вам нужны и откуда взялись данные: кто их собирал, когда, о чём и зачем.